Many communication networks, such as the Internet, rely on packet switching technologies (e.g., X.25, frame relay, asynchronous transfer mode, etc.) to transport variable or uniform blocks (usually termed packets or cells) of data between nodes. The term packet will be used herein to collectively refer to any such block of information. Such networks generally perform two major functions: routing and congestion control. The object of routing is to deliver, correctly and sometimes in sequence, the packets from a source to a destination. The object of congestion control is to maintain the number of packets within the network (or a region or sub-network thereof) below a level at which queuing delays become excessive. Often, where queuing delays are significant, packets are dropped.
In essence, a packet switched network is a network of queues communicatively coupled together by communication links (which may be made up of various physical media). At each network node (e.g., a switch or router), there exists one or more queues of packets for each outgoing link. If the rate at which packets arrive and queue up exceeds the rate at which packets are transmitted, queue size grows without bound and the delay experienced by a packet tends towards infinity. Even if the packet arrival rate is less than the packet transmission rate, queue length may grow dramatically as the arrival rate approaches the transmission rate.
In an ideal case, network throughput, and hence network use, should increase to an offered load up to the physical capacity of the network and remain at capacity if the load is further increased. This ideal case, however, requires that all nodes somehow know the timing and rate of packets that will be presented to the network with no overload and no delay in acquiring this information; a situation which is not possible. If no congestion control is exercised, as the load increases, use increases for a while. Then, as the queue lengths at various nodes begins to grow, throughput actually drops. This is due to the fact that the queues are constrained to a finite length by the physical size of the memories in which they exist. When a node's memory (i.e., its queues) is full, it must drop (i.e., discard) additional incoming packets. Thus, the source is forced to retransmit these packets in addition to any new packets it might have. This only serves to worsen the situation. As more and more packets are retransmitted, the load on the network grows and more and more nodes become saturated. Eventually, even a successfully delivered packet may be retransmitted because it takes so long to get to its destination (whereupon it may be acknowledged by the destination node) that the source actually assumes that the packet was lost and it tries again. Under such circumstances, the effective capacity of the network is virtually zero.
Contrary to what one might believe, the solution to this problem is not to simply allow the queue lengths to grow indefinitely. Indeed, it has been shown that even where queue lengths are allowed to be infinite, congestion can occur. See, e.g., John Nagle, “On Packet Switches with Infinite Storage”, Network Working Group, Internet Engineering Task Force, RFC 970 (1985). One reason that this is true is that packets are often coded with an upper bound on their life, thus causing expired packets to be dropped and retransmitted, adding to the already overwhelming volume of traffic within the network.
It is clear that catastrophic network failures due to congestion should (indeed, must) be avoided and preventing such failures is the task of congestion control processes within packet switched networks. To date, however, the object of such congestion control processes has been to limit queue lengths at the various network nodes so as to avoid throughput collapse. Such techniques require the transmission of some control information between the nodes and this overhead itself tends to limit the available network bandwidth for data traffic. Nevertheless, a good congestion control process maintains a throughput that differs from a theoretical ideal by an amount roughly equal to its control overhead.
In addition to imposing limits on the true available throughout of a network, conventional congestion control processes do not take into account the true nature of network traffic. Existing approaches have generally viewed network traffic (e.g., the generation of new packets to be injected into a network) as essentially random processes. However, recent work in the area of traffic modeling has shown that network traffic is in fact fractal in nature. None of the currently proposed congestion control methodologies capture or exploit this characteristic.
The concept of fractality can be illustrated in Cantor Sets. Consider a line segment of length 1 unit. Now divide this line segment into three equal parts and remove the middle third. Two smaller segments of length ⅓ unit remain. Now divide each of these segments into three again and remove the corresponding middle thirds. In this generation of line segments there are four separate segments, each of length 1/9 unit. This process can be repeated ad infinitum, with a basic pattern appearing in each generation of line segments at all scales. This construction of so-called Cantor Sets is fractal. Mathematically, the degree of fractality can be stated by a measure known as the fractal dimension.
Network traffic, including Internet traffic, exhibits the same sort of fractal properties as the Cantor Sets of line segments described above. That is, it has been discovered that when a measure of data units (e.g., bits) per time interval is plotted against time, a persistent behavior is noted at all time scales. So, a plot of bits/hour versus hours shows the same persistent pattern as a plot of bits/minute versus minutes, and bits/second versus seconds and so on. If traffic flow in a network were truly random (as had been postulated in the past and upon which assumptions current congestion control methodologies were based), then at some (large) time scale, burstiness should appear. This burstiness should then disappear as the time scale is reduced, resulting in a random distribution. The experiments mentioned above, however, have shown that this does not occur. Instead, the same persistent patterns of traffic flow that are present at large time scales are observed at small time scales. Furthermore, the traffic flow (i.e., the number of bytes per unit of time) is chaotic. The degree of chaoticness can by quantified by the mathematical concept called fractal dimension. With this range of fractal dimension, the applicant has discovered that the chaos of the traffic flow can be controlled using the methods described below.
As indicated above, current congestion control processes simply do not take the fractal network traffic characteristics into account and, therefore, cannot be expected to be optimum solutions to the congestion problem. What is needed therefore, is a congestion control scheme which does account for the fractal nature of network traffic flow.